B'There are n points marked on the plane. The points are situated in such a way that they form a regular polygon (marked points are its vertices, and they are numbered in counter-clockwise order). You can draw n xe2 x80 x89- xe2 x80 x891 segments, each connecting any two marked points, in such a way that all points have to be connected with each other (directly or indirectly). But there are some restrictions. Firstly, some pairs of points cannot be connected directly and have to be connected undirectly. Secondly, the segments you draw must not intersect in any point apart from the marked points (that is, if any two segments intersect and their intersection is not a marked point, then the picture you have drawn is invalid). How many ways are there to connect all vertices with n xe2 x80 x89- xe2 x80 x891 segments? Two ways are considered different iff there exist some pair of points such that a segment is drawn between them in the first way of connection, but it is not drawn between these points in the second one. Since the answer might be large, output it modulo 109 xe2 x80 x89+ xe2 x80 x897. The first line contains one number n (3 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89500) -- the number of marked points. Then n lines follow, each containing n elements. ai, xe2 x80 x89j (j-th element of line i) is equal to 1 iff you can connect points i and j directly (otherwise ai, xe2 x80 x89j xe2 x80 x89= xe2 x80 x890). It is guaranteed that for any pair of points ai, xe2 x80 x89j xe2 x80 x89= xe2 x80 x89aj, xe2 x80 x89i, and for any point ai, xe2 x80 x89i xe2 x80 x89= xe2 x80 x890. Print the number of ways to connect points modulo 109 xe2 x80 x89+ xe2 x80 x897. '...